Separating a Real-Life Nonlinear Image Mixture

When acquiring an image of a paper document, the image printed on the back page sometimes shows through. The mixture of the front- and back-page images thus obtained is markedly nonlinear, and thus constitutes a good real-life test case for nonlinear blind source separation. This paper addresses a difficult version of this problem, corresponding to the use of "onion skin" paper, which results in a relatively strong nonlinearity of the mixture, which becomes close to singular in the lighter regions of the images. The separation is achieved through the MISEP technique, which is an extension of the well known INFOMAX method. The separation results are assessed with objective quality measures. They show an improvement over the results obtained with linear separation, but have room for further improvement

Using seismic mixtures to extract tilts and recover estimates of ground displacements

One of the goals of seismology is to understand the behaviour of the earth’s movements during the occurrence of an earthquake. This research focuses on the recovery of better estimation of the true ground displacements as the tilt components are inherent in recorded acceleration time histories. The raw acceleration time histories recorded in seismograms of the near field earthquake are contaminated by the effects of tilt time histories. The effects of tilt time histories cause non–zero baseline errors in seismic records thereby providing offset in the ground velocity although the final velocity never ends to zero and ground displacement diverges from the constant value. To perform baseline corrections it is therefore necessary to remove the tilt and noise components. Tilt separation was undertaken using a model designated the Tilt Separation – Independent Component Analysis (TS-ICA) model, and an enhanced version of the Extended Generalised Beta Distribution (EGBD) model. Several source distributions such as Normal, Gaussian, Non-Gaussian, Sub and Super Gaussian and skewed distribution with zero kurtosis has been modelled using EGBD and separated using EGBD-ICA. In order to refine the EGBD-ICA model, a randomised mixing matrix was introduced in the existing EGBD-ICA model using MATLAB. With the introduction of the mixing matrix, the consistency of the source separation has improved and particularly tilt separation was convincing for both artificial tilt separation from the Hector Mine earthquake data and real-time tilt separation from the real-time acceleration time histories. The tilt separation and de-noising by the TS-ICA model has given better estimates of ground displacement than the tilt contaminated ground displacement. The estimated tilt angle can provide further scope for seismic scientists and civil engineers to improve their understanding of the tilt behaviour during an earthquake and can add another dimension to their research by making it possible to improve the stability of the building structures in the seismically active regions and areas which are potentially prone to earthquake

Advances in variational Bayesian nonlinear blind source separation

Linear data analysis methods such as factor analysis (FA), independent component analysis (ICA) and blind source separation (BSS) as well as state-space models such as the Kalman filter model are used in a wide range of applications. In many of these, linearity is just a convenient approximation while the underlying effect is nonlinear. It would therefore be more appropriate to use nonlinear methods. In this work, nonlinear generalisations of FA and ICA/BSS are presented. The methods are based on a generative model, with a multilayer perceptron (MLP) network to model the nonlinearity from the latent variables to the observations. The model is estimated using variational Bayesian learning. The variational Bayesian method is well-suited for the nonlinear data analysis problems. The approach is also theoretically interesting, as essentially the same method is used in several different fields and can be derived from several different starting points, including statistical physics, information theory, Bayesian statistics, and information geometry. These complementary views can provide benefits for interpretation of the operation of the learning method and its results. Much of the work presented in this thesis consists of improvements that make the nonlinear factor analysis and blind source separation methods faster and more stable, while being applicable to other learning problems as well. The improvements include methods to accelerate convergence of alternating optimisation algorithms such as the EM algorithm and an improved approximation of the moments of a nonlinear transform of a multivariate probability distribution. These improvements can be easily applied to other models besides FA and ICA/BSS, such as nonlinear state-space models. A specialised version of the nonlinear factor analysis method for post-nonlinear mixtures is presented as well.reviewe

Advanced source separation methods with applications to spatio-temporal datasets

Latent variable models are useful tools for statistical data analysis in many applications. Examples of popular models include factor analysis, state-space models and independent component analysis. These types of models can be used for solving the source separation problem in which the latent variables should have a meaningful interpretation and represent the actual sources generating data. Source separation methods is the main focus of this work. Bayesian statistical theory provides a principled way to learn latent variable models and therefore to solve the source separation problem. The first part of this work studies variational Bayesian methods and their application to different latent variable models. The properties of variational Bayesian methods are investigated both theoretically and experimentally using linear source separation models. A new nonlinear factor analysis model which restricts the generative mapping to the practically important case of post-nonlinear mixtures is presented. The variational Bayesian approach to learning nonlinear state-space models is studied as well. This method is applied to the practical problem of detecting changes in the dynamics of complex nonlinear processes. The main drawback of Bayesian methods is their high computational burden. This complicates their use for exploratory data analysis in which observed data regularities often suggest what kind of models could be tried. Therefore, the second part of this work proposes several faster source separation algorithms implemented in a common algorithmic framework. The proposed approaches separate the sources by analyzing their spectral contents, decoupling their dynamic models or by optimizing their prominent variance structures. These algorithms are applied to spatio-temporal datasets containing global climate measurements from a long period of time.reviewe

Méthodes de séparation aveugle de sources non linéaires, étude du modèle quadratique 2X2

Cette thèse présente des méthodes de séparation aveugle de sources pour un modèle de mélange non-linéaire particulier, le cas quadratique avec auto-termes et termes croisés. Dans la première partie, nous présentons la structure de séparation étudiée qui se décline sous deux formes : étendue ou basique. Les propriétés de ce réseau récurrent sont ensuite analysées (points d'équilibre, stabilité locale). Nous proposons alors deux méthodes de séparation aveugle de sources. La première exploite les cumulants des observations en un bloc placé en amont de la structure récurrente. La deuxième méthode est basée sur une approche par maximum de vraisemblance. Le tout est validé par des simulations numériques.This thesis presents blind source separation (BSS) methods for a particular model of mixture, the quadratic one. The first part presents the separating structure (basic and extended versions).The equilibrium points of the structure and their local stability are then studied. We propose two methods of BSS. The first method uses the cumulants and the second is based on a maximum likelihood approach. We validate our results by numerical tests

Exploratory source separation in biomedical systems

Contemporary science produces vast amounts of data. The analysis of this data is in a central role for all empirical sciences as well as humanities and arts using quantitative methods. One central role of an information scientist is to provide this research with sophisticated, computationally tractable data analysis tools. When the information scientist confronts a new target field of research producing data for her to analyse, she has two options: She may make some specific hypotheses, or guesses, on the contents of the data, and test these using statistical analysis. On the other hand, she may use general purpose statistical models to get a better insight into the data before making detailed hypotheses. Latent variable models present a case of such general models. In particular, such latent variable models are discussed where the measured data is generated by some hidden sources through some mapping. The task of source separation is to recover the sources. Additionally, one may be interested in the details of the generation process itself. We argue that when little is known of the target field, independent component analysis (ICA) serves as a valuable tool to solve a problem called blind source separation (BSS). BSS means solving a source separation problem with no, or at least very little, prior information. In case more is known of the target field, it is natural to incorporate the knowledge in the separation process. Hence, we also introduce methods for this incorporation. Finally, we suggest a general framework of denoising source separation (DSS) that can serve as a basis for algorithms ranging from almost blind approach to highly specialised and problem-tuned source separation algoritms. We show that certain ICA methods can be constructed in the DSS framework. This leads to new, more robust algorithms. It is natural to use the accumulated knowledge from applying BSS in a target field to devise more detailed source separation algorithms. We call this process exploratory source separation (ESS). We show that DSS serves as a practical and flexible framework to perform ESS, too. Biomedical systems, the nervous system, heart, etc., constitute arguably the most complex systems that human beings have ever studied. Furthermore, the contemporary physics and technology have made it possible to study these systems while they operate in near-natural conditions. The usage of these sophisticated instruments has resulted in a massive explosion of available data. In this thesis, we apply the developed source separation algorithms in the analysis of the human brain, using mainly magnetoencephalograms (MEG). The methods are directly usable for electroencephalograms (EEG) and with small adjustments for other imaging modalities, such as (functional) magnetic resonance imaging (fMRI), too.reviewe